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pro vyhledávání: '"Said, Ayman R."'
Fix a bounded, analytic, and simply connected domain $\Omega\subset\mathbb{R}^2.$ We show that all analytic steady states of the Euler equations with stream function $\psi$ are either radial or solve a semi-linear elliptic equation of the form $\Delt
Externí odkaz:
http://arxiv.org/abs/2408.14662
We introduce a local-in-time existence and uniqueness class for solutions to the 2d Euler equation with unbounded vorticity. Furthermore, we show that solutions belonging to this class can develop stronger singularities in finite time, meaning that t
Externí odkaz:
http://arxiv.org/abs/2312.17610
Autor:
Jeong, In-Jee, Said, Ayman R.
We study logarithmic spiraling solutions to the 2d incompressible Euler equations which solve a nonlinear transport system on $\mathbb{S}$. We show that this system is locally well-posed in $L^p, p\geq 1$ as well as for atomic measures, that is logar
Externí odkaz:
http://arxiv.org/abs/2302.09447
We study the long-time behavior of scale-invariant solutions of the 2d Euler equation satisfying a discrete symmetry. We show that all scale-invariant solutions with bounded variation on $\mathbb{S}^1$ relax to states that are piece-wise constant wit
Externí odkaz:
http://arxiv.org/abs/2211.08418
Akademický článek
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